package com.linc.multithread.logic;

import java.math.BigDecimal;

/**
 * Created by linc on 18-9-15.
 */

public class PiMaker {

    // constant used in pi computation
    private static final BigDecimal FOUR = BigDecimal.valueOf(4);

    // rounding mode to use during pi computation
    private static final int roundingMode = BigDecimal.ROUND_HALF_EVEN;

    /**
    * Compute the value of pi to the specified number of digits after the
    * decimal point. The value is computed using Machin's formula:
    *
    * pi/4 = 4*arctan(1/5)-arctan(1/239)
    *
    * and a power series expansion of arctan(x) to sufficient precision.
    */
    public static BigDecimal computePi(int digits)
    {
        try {
            Thread.sleep(2000);
        } catch (InterruptedException e) {
            e.printStackTrace();
        }
        int scale = digits + 5;
        BigDecimal arctan1_5 = arctan(5, scale);
        BigDecimal arctan1_239 = arctan(239, scale);
        BigDecimal pi = arctan1_5.multiply(FOUR).
                subtract(arctan1_239).multiply(FOUR);
        return pi.setScale(digits, BigDecimal.ROUND_HALF_UP);
    }

    /**
    * Compute the value, in radians, of the arctangent of the inverse of
    * the supplied integer to the specified number of digits after the
    * decimal point. The value is computed using the power series
    * expansion for the arc tangent:
    *
    * arctan(x) = x-(x^3)/3+(x^5)/5-(x^7)/7+(x^9)/9 ...
    */
    public static BigDecimal arctan(int inverseX, int scale)
    {
        BigDecimal result, numer, term;
        BigDecimal invX = BigDecimal.valueOf(inverseX);
        BigDecimal invX2 = BigDecimal.valueOf(inverseX * inverseX);
        numer = BigDecimal.ONE.divide(invX, scale, roundingMode);
        result = numer;
        int i = 1;
        do
        {
            numer = numer.divide(invX2, scale, roundingMode);
            int denom = 2 * i + 1;
            term = numer.divide(BigDecimal.valueOf(denom), scale,
                    roundingMode);
            if ((i % 2) != 0)
                result = result.subtract(term);
            else
                result = result.add(term);
            i++;
        }
        while (term.compareTo(BigDecimal.ZERO) != 0);
        return result;
    }


}
